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I have a dataset of 50 features that resulted after PCA was employed (originally, the dataset had 343 features. The 50 features are the principal components obtained with PCA). Does it make sense to apply feature selection on those 50 features to choose the top 10 features?

Thank you,

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  • $\begingroup$ Just to make sure, the original dataset had 50 features (PCA does not change the number of features, just the content thereof)? $\endgroup$ – Richard Hardy May 9 '20 at 17:36
  • $\begingroup$ No, the dataset originally had 343 features. I will revise my post. $\endgroup$ – Dave May 9 '20 at 17:38
  • $\begingroup$ How did you determine the number of PCs to keep, i.e. why 50? $\endgroup$ – Richard Hardy May 9 '20 at 17:41
  • $\begingroup$ @RichardHardy For security reasons, the dataset was given to me after being PCA transformed into 50 features which are the principal components obtained with PCA. $\endgroup$ – Dave May 9 '20 at 17:42
  • $\begingroup$ Then it can make sense to apply feature selection. But why 10? Is that a magic number? $\endgroup$ – Richard Hardy May 9 '20 at 17:44
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Yes, it may very well make sense to do feature selection after PCA. PCA often yields a small number of components that explain a large fraction of variance in the data. Discarding the low-variance components and keeping only the high-variance components for future analysis can offer good a good balance w.r.t. the bias-variance tradeoff. In fact, PCA is often used precisely for that.

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